Righting Reflex in Cats

Cats possess the righting reflex which allows them to always land on their feet after a fall, even if they are dropped with their back towards the ground. At first, this ability may seem like it violates the Law of Conservation of Angular Momentum; the cat starts with zero angular momentum and no external force acts on it, so it must turn its self over while maintaining zero angular momentum. To achieve this, a cat will bend its back, creating two different axes of rotation on its body, one on its front half and one on its back half. Next, the cat will tuck its front legs towards itself, lowering the moment of inertia of the front half, and rotate so its front half is facing the ground. Simultaneously, the cat will stretch its hind legs out, increasing the moment of inertia of its back half while it rotates in the opposite direction as the front half did to maintain zero angular momentum. Due to the back half's large inertia, the angular velocity of the back half will not be as big as the front half's and it will not rotate as much. Once the front half of the cat is facing the ground, the cat will rotate its hind legs to face the ground. To do this, the cat will straighten the front legs, increasing the moment of inertia and lowering the angular velocity. The hind legs are brought into the body, lowering the moment of inertia and increasing angular velocity. As a result, the rear end of body rotates to face the ground while the front half barely rotates due to its large inertia.

I_aω_a + Ibωb = L = 0

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